Alphabet-almost-simple 2-neighbour-transitive codes
| Autor: | Daniel R. Hawtin, Neil I. Gillespie |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Alphabet-almost-simple
Discrete mathematics Code (set theory) Transitive relation Algebra and Number Theory 2-neighbour-transitive 010102 general mathematics Transitive closure Hamming distance 0102 computer and information sciences 01 natural sciences Transitive reduction Theoretical Computer Science Combinatorics Hamming graph 010201 computation theory & mathematics Automorphism groups Discrete Mathematics and Combinatorics Hamming(7 4) Geometry and Topology 0101 mathematics Hamming weight Completely transitive Mathematics |
| Zdroj: | Gillespie, N I & Hawtin, D R 2018, ' Alphabet-almost-simple 2-neighbour-transitive codes ', Ars Mathematica Contemporanea, vol. 14, no. 2, pp. 345-357 . < http://amc-journal.eu/index.php/amc/article/view/1240 > Ars mathematica contemporanea |
| ISSN: | 1855-3974 1855-3966 |
| Popis: | Let X be a subgroup of the full automorphism group of the Hamming graph H ( m , q ) , and C a subset of the vertices of the Hamming graph. We say that C is an ( X , 2) -neighbour-transitive code if X is transitive on C , as well as C 1 and C 2 , the sets of vertices which are distance 1 and 2 from the code. It has been shown that, given an ( X , 2) -neighbour-transitive code C , there exists a subgroup of X with a 2 -transitive action on the alphabet; this action is thus almost-simple or affine. This paper completes the classification of ( X , 2) -neighbour-transitive codes, with minimum distance at least 5 , where the subgroup of X stabilising some entry has an almost-simple action on the alphabet in the stabilised entry. The main result of this paper states that the class of ( X , 2) neighbour-transitive codes with an almost-simple action on the alphabet and minimum distance at least 3 consists of one infinite family of well known codes. |
| Databáze: | OpenAIRE |
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